If Boyle re-signs with the Islanders, the draft pick improves to a fourth-round selection.
Earlier this week, Newsday's Arthur Staple reported that Boyle will let the Islanders know by the end of the week if he even intends to entertain contract discussions with the club.
Boyle, 37, is set to become an unrestricted free agent July 1.
Boyle's agent, George Bazos, however, told TFP on Friday that his client has not yet made up his mind.
Boyle has spoken to a number of different Islanders players about their time with the team and may head to Long Island to visit with the club next week.
The Islanders have presented Boyle with some contract terms, but Bazos confirmed that not real negotiations have started yet, and won't if Boyle is not interested in pursuing them.